Problem: A group of neighbors is holding an end of summer block party. They buy $p$ packs of hot dogs, with $8$ hot dogs in each pack. All together, they have $56$ hot dogs for the party. Write an equation to describe this situation. How many packs of hot dogs did the neighbors buy?
There are $8$ hot dogs in each pack. We are calling the number of packs of hot dogs ${p}$. There were a total of ${56}$ hot dogs at the party. We can represent the total number of hot dogs at the party as a product: ${8} {p}$ We know that there were a total of ${56}$ hot dogs at the party. We can set these two expressions equal to describe this situation with an equation: ${8} {p} = {56}$ Other ways to represent the situation with an equation include: $\dfrac{{56}}{ p}=8$ or $\dfrac{{56}}{ 8}= p$. Now we can solve for ${p}$. Divide both sides by ${8}$ to get $ p$ by itself. $\begin{aligned}\dfrac{ {8}{p}}{8} &= \dfrac{{56}}{8} \\\\ {p} &= 7 \end{aligned}$ The following equation matches this situation: $8p=56$ The neighbors bought $7$ packs of hot dogs.